In PTL 1, a projection type display device (projector) which projects a projected screen on a screen and captures an image including an object such as a finger by a camera so as to make it possible to detect a position of the object using the captured image is disclosed. The object such as the finger is used as the pointing element for giving an instruction to the projected screen. That is, when a tip of the object is in contact with the screen, the projector recognizes that a predetermined instruction such as rendering is input to the projected screen and re-renders the projected screen according to the instruction. Accordingly, the user is able to input various instructions by using the projected screen as a user interface. As such, a type of projector capable of using the projected screen on the screen as a user interface by which input can be made is called an “interactive projector”. An object used for giving an instruction to the projected screen is called a “pointing element”.